What’s Real About the Business Cycle? James D. Hamilton This paper argues that a linear statistical model with homoskedastic errors cannot capture the nineteenth-century notion of a recurring cyclical pattern in key economic aggregates. A simple nonlinear alternative is proposed and used to illustrate that the dynamic behavior of unemployment seems to change over the business cycle, with the unemployment rate rising more quickly than it falls. Furthermore, many but not all economic downturns are also accompanied by a dramatic change in the dynamic behavior of short-term interest rates. It is suggested that these nonlinearities are most naturally interpreted as resulting from short-run failures in the employment and credit markets and that understanding these short-run failures is the key to understanding the nature of the business cycle. Federal Reserve Bank of St. Louis Review, July/August 2005, 87(4), pp. 435-52. WHAT IS THE BUSINESS CYCLE? In part, this shift in the profession’s concep- tion of what needs to be explained about business he term “cycle” is used to describe a fluctuations reflects a desire to integrate the deter- process that moves sequentially between minants of long-run economic growth and the a series of clearly identifiable phases in a T causes of short-run economic downturns within recurrent or periodic fashion. Economists of the a single unified theory of aggregate economic per- nineteenth and early twentieth centuries were formance. Since improvements in overall produc- persuaded that they saw such a pattern exhib- tivity are widely acknowledged to be one of the ited in the overall level of economic activity key factors driving long-run growth, and since and enthusiastically sought to characterize the observed regularities of what came to be known such improvements cannot reasonably be expected as the “business cycle.” The most systematic to occur at a constant rate over time, it is natural and still-enduring summaries of what seems to to explore the possibility that variation over time happen during the respective phases were pro- in the rate of technological progress could be a vided by Mitchell (1927, 1951) and Burns and primary cause of variation over time in the level Mitchell (1946). of economic activity. Brock and Mirman (1972) The expression “business cycle theory” were the first to incorporate stochastic variation remains in common usage today, even though, in in the rate of technical progress into a neoclassical most of the modern models that wear the label, growth model, though they clearly intended this there in fact is no business cycle in the sense just as a model of long-run growth rather than a realis- described. These are models of economic fluctu- tic description of short-run fluctuations. Kydland ations, to be sure, but they do not exhibit clearly and Prescott (1982) later took the much bolder articulated phases through which the economy step of proposing that this class of models might could be said to pass in a recurrent pattern. explain variations in economic activity at all fre- James D. Hamilton is a professor of economics at the University of California, San Diego. This research was supported by the National Science Foundation under grant No. SES-0215754. © 2005, The Federal Reserve Bank of St. Louis. Articles may be reprinted, reproduced, published, distributed, displayed, and transmitted in their entirety if copyright notice, author name(s), and full citation are included. Abstracts, synopses, and other derivative works may be made only with prior written permission of the Federal Reserve Bank of St. Louis. FEDERAL RESERVE BANK OF ST. LOUIS REVIEW JULY/AUGUST 2005 435 Hamilton quencies, in what has come to be known as “real whether the nineteenth-century economists were business cycle models.” on to something that their modern descendants Although unifying growth and business cycle may have forgotten. Is there really a business cycle, theory holds tremendous aesthetic appeal, this or is the expression an unfortunate linguistic particular solution is not without its detractors. vestige of a less-informed era? I will argue that Indeed, the reasons that Irving Fisher gave in 1932 indeed there is a recurring pattern in the level of for rejecting such an approach have in the opinion economic activity that needs to be explained, but of many yet to receive a satisfying response from that a statistical characterization of this pattern modern real business cycle theorists: requires a nonlinear dynamic representation and calls for an asymmetric interpretation of the forces [I]n times of depression, is the soil less fertile? that cause employment to rise and fall. I further Not at all. Does it lack rain? Not at all. Are the observe that one element of this pattern has often mines exhausted? No, they can perhaps pour been a related cyclical behavior of interest rates. out even more than the old volume of ore, if To the question, “Is the business cycle real?” anyone will buy. Are the factories, then, lamed these findings suggest that, yes, the business cycle in some way—down at the heel? No; machinery is real in the sense that it is a feature of the data and invention may be at the very peak. that needs to be explained. In the other meaning (Fisher, 1932, p. 5) of the term “real,” however—the sense from which Continuing along the lines of Fisher’s reason- springs the label “real business cycle,” namely, a ing, the size of the population places an obvious cycle unrelated to monetary developments—the physical limit on how much a given nation can evidence adduced here for the importance of produce and is certainly a key reason that aggre- comovements between financial and real variables gate output increases over time. But just as surely, suggests that the cycle is not “real” at all or, at the a decrease in population is not the cause of the least, not completely divorced from monetary decrease in employment that we observe in times developments. when the unemployment rate is shooting up dra- matically. There is in this respect an obvious inherent asymmetry in fluctuations in the number THE BEHAVIOR OF of workers employed—the measure must go up UNEMPLOYMENT for different reasons than it goes down. A parallel Figure 1 plots the monthly unemployment rate argument can be made in terms of the capital in the United States from 1948:01 to 2004:03.1 I stock, another key factor determining long-run would suggest that someone looking at such a growth, which again places an upper limit on graph for the first time would indeed be inclined how much a country can produce. Yet in times to identify a repeated sequence of ups and downs, when we see all measures of capacity utilization with each of the obvious sharp upswings in the falling, the natural inference is that some forces unemployment rate occurring during periods that other than the quantity or quality of available the National Bureau of Economic Research (NBER) manufacturing facilities account for the drop in has classified as economic recessions (indicated aggregate output. by shaded regions on the graph). If we agree that these three factors—technol- Although one’s eye is sympathetic to the claim ogy, labor force, and the capital stock—are the that these data display a recurrent pattern, it does three main determinants of long-run economic not appear to be cyclical in the sense of exhibiting growth, we might greet with considerable skepti- strict periodicity. For example, the two consecu- cism the suggestion that the same three factors tive unemployment peaks in 1958:07 and 1961:05 are in a parallel way responsible for producing are separated by less than three years, whereas the drop in real GDP that we observe during a business downturn. 1 This is the seasonally adjusted civilian unemployment rate from The purpose of this paper is to explore the Bureau of Labor Statistics; http://stats.bls.gov. 436 JULY/AUGUST 2005 FEDERAL RESERVE BANK OF ST. LOUIS REVIEW Hamilton Figure 1 Figure 2 U.S. Monthly Civilian Unemployment Rate Estimated Spectrum of U.S. Monthly Civilian and U.S. Recessions, 1948:01–2004:03 Unemployment Rate, 1948:01–2004:03 11 14 10 12 10 9 8 8 6 7 4 2 6 0 5 0 10 20 30 Period of Cycle (years) 4 3 NOTE: Plotted as a function of the period of the cycle in years. 2 1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003 (2) uyc y y tt=−−φφ11 t−− − 22 t k log12 / log / 2 =+{}ΓΓ()νν − {}[] those of 1982:11 and 1992:06 are separated by a (3) 12/log2 decade. More formally, one can look for any sort −()()σνπ of periodic pattern by examining the spectrum of 2 with respect to θ = (c,φ1,φ2,σ ,ν)′ subject to the the unemployment rate, an estimate of which is constraints3 that σ 2 > 0 and ν > 0. These maximum plotted in Figure 2 as a function of the period of likelihood estimates (MLEs) (with asymptotic the cycle.2 If one tries to decompose the unem- standard errors in parentheses) imply that the ployment series in Figure 1 into a series of strictly unemployment rate yt for month t could be mod- periodic cycles, by far the most important of these eled as follows: are those with the longest period, as opposed to (4) yytt++0.. 060 1 1171 − 0 . 128 yvtt2 + 0., 158 something regularly repeating every 3 to 5 years. ()()0.. 028 0 037 − (()0 . 037 − ()0. 007 Let yt denote the unemployment rate. Consider where vt is distributed Student t with 4.42 degrees an AR(2) representation of these data with Student of freedom, with the standard error for the degrees- t innovations, obtained by maximizing the log of-freedom parameter ν being estimated at 0.74.